Class Lattice

Inheritance Relationships

Derived Types

Class Documentation

class brille::Lattice

A class to hold information about a space-spanning lattice in three dimensions.

A space-spanning lattice in N dimensions has N basis vectors which can be described fully by their N lengths and the sum(1:N-1) angles between each set of basis vectors, or sum(1:N) scalars in total. Storing only their lengths and angles is therefore always more efficient than storing all N² components of the basis vectors in an orthonormal frame. This class stores the 3 lengths and 3 angles required to describe a 3 dimensional space-spanning lattice, plus the volume of the lattice unit cell and an optional Hall number if a non-Primitive lattice is desired.

Subclassed by brille::Direct, brille::Reciprocal

Public Functions

Lattice(const std::array<double, 3> &l, const std::array<double, 3> &a, const Bravais b, const Symmetry sgs, const PointSymmetry pgs, const Basis base)

Construct the Lattice from its components, excluding the volume which is calculated.

Lattice(const double*, const int h = 1)

Construct the Lattice from a matrix of the basis vectors.

Lattice(const brille::Array2<double> &latmat, const std::vector<std::array<double, 3>> &pos, const std::vector<unsigned long> &typ, const Symmetry &sym)

Construct the Lattice from an Array2 3x3 basis vector matrix, plus basis and symmetry information.

template<class I>
Lattice(const double *latmat, std::vector<I> &strides, const int h)

Construct the Lattice from a possibly-not-contiguous matrix of the basis vectors.

template<class I>
Lattice(const double *lengths, std::vector<I> &lenstrides, const double *angles, std::vector<I> &angstrides, const int h, const AngleUnit au = AngleUnit::not_provided)

Construct the lattice from two vectors of the lengths and angles.

Parameters

  • lengths: A pointer to the first of three basis vector lengths in arbitrary length units

  • lenstrides: The first element must contain the stride in bytes between basis vector lenght entries

  • angles: A pointer to the first of three inter-basis-vector angles in units of pi, radian, or degree

  • angstrides: The first element must contain the stride in bytes between angle entries

  • h: The hall number specifying the lattice symmetries

  • au: An enum which identifies which units the provided angles use. If omitted or AngleUnit::not_provided, an attempt is made to guess the units. If all provided angles have values less than π then they are assumed to be in units of radian, otherwise they are assumed to be in units of degrees.

Lattice(const double*, const double*, const int h = 1, const AngleUnit au = AngleUnit::not_provided)

Construct the Lattice from a vector of the basis vector lengths and a vector of the basis vector angles.

Lattice(const double la = 1.0, const double lb = 1.0, const double lc = 1.0, const double al = brille::halfpi, const double bl = brille::halfpi, const double cl = brille::halfpi, const int h = 1)

Construct the Lattice from the three scalar lengths and three scalar angles.

Lattice(const double*, const std::string&, const std::string &choice = "")

Construct the Lattice from a matrix of the basis vectors, specifying an International Tables symmetry name instead of a Hall number.

Lattice(const double*, const double*, const std::string&, const std::string &choice = "", const AngleUnit au = AngleUnit::not_provided)

Construct the lattice from vectors, specifying an International Tables symmetry name instead of a Hall number.

template<class I>
Lattice(const double *latmat, std::vector<I> &strides, const std::string &itname, const std::string &choice = "")
template<class I>
Lattice(const double *lengths, std::vector<I> &lenstrides, const double *angles, std::vector<I> &angstrides, const std::string &itname, const std::string &choice = "", const AngleUnit au = AngleUnit::not_provided)

Construct the lattice from two possibly-not-contiguous vectors of the lengths and angles.

Lattice(const double, const double, const double, const double, const double, const double, const std::string&, const std::string &choice = "")

Construct the lattice from scalars, specifying an International Tables symmetry name instead of a Hall number.

~Lattice() = default
double get_a() const

Return the first basis vector length.

double get_b() const

Return the second basis vector length.

double get_c() const

Return the third basis vector length.

double get_alpha() const

Return the angle between the second and third basis vectors in radian.

double get_beta() const

Return the angle between the first and third basis vectors in radian.

double get_gamma() const

Return the angle between the first and second basis vectors in radian.

double get_volume() const

Return the volume of the parallelpiped unit cell formed by the basis vectors.

double calculatevolume()

Calculate and return the unit cell volume.

void get_metric_tensor(double *mt) const

Calculate the metric tensor of the Lattice

Parameters

  • [out] mt: Pointer to memory which can store 9 doubles

void get_covariant_metric_tensor(double *mt) const

Calculate the covariant metric tensor of the Lattice this is typically referred to as the metric tensor

Parameters

  • [out] mt: Pointer to memory which can store 9 doubles

void get_contravariant_metric_tensor(double *mt) const

Calculate the contravariant metric tensor of the Lattice the inverse of the metric tensor

Parameters

  • [out] mt: Pointer to memory which can store 9 doubles

std::vector<double> get_metric_tensor() const

Calculate the metric tensor of the Lattice

Return

A std::vector of the row-ordered matrix

std::vector<double> get_covariant_metric_tensor() const

Calculate the covariant metric tensor of the Lattice this is typically referred to as the metric tensor

Return

A std::vector of the row-ordered matrix

std::vector<double> get_contravariant_metric_tensor() const

Calculate the contravariant metric tensor of the Lattice the inverse of the metric tensor

Return

A std::vector of the row-ordered matrix

bool issame(const Lattice&) const

Determine if the passed Lattice represents the same space-spanning lattice.

bool isapprox(const Lattice&) const

Determine if the passed Lattice represents an equivalent space-spanning lattice within the specified tolerance. Simultaneous permutations of lengths and angles are considered as equivalent e.g., (a,b,c)(α,β,γ) ≡ (b,c,a)(β,γ,α) ≡ (c,a,b)(γ,α,β), as are antipermutations, e.g., (a,b,c)(α,β,γ) ≡ (a,c,b)(α,γ,β) ≡ (c,b,a)(γ,β,α) ≡ (b,a,c)(β,α,γ).

int ispermutation(const Lattice&) const

Determine if the passed Lattice is a permutation of the space-spanning lattice within the specified tolerance. The equivalence is encoded in a signed integer:

void print()

Print the basis vector lengths and angles to the console.

std::string string_repr()

Return a string representation of the basis vector lengths and angles.

Bravais get_bravais_type() const

Return the Bravais centring of the Lattice.

Bravais set_bravais_type(const Bravais b)

Set the Bravais centring of the Lattice.

Symmetry get_spacegroup_symmetry(const int time_reversal = 0) const

Return the Spacegroup symmetry operation object of the Lattice.

Symmetry set_spacegroup_symmetry(const Symmetry &gens)

Set the Spacegroup symmetry operation object also sets PointSymmetry.

PointSymmetry get_pointgroup_symmetry(const int time_reversal = 0) const

Return the Pointgroup Symmetry operation object of the Lattice.

bool has_space_inversion() const

Check whether the pointgroup has the space-inversion operator, ̄1.

Basis get_basis() const
Basis set_basis(const std::vector<std::array<double, 3>> &pos, const std::vector<unsigned long> &typ)
Basis set_basis(const Basis &b)

Protected Functions

double unitvolume() const
Lattice inner_star() const
template<class I>
void set_len_pointer(const double *lvec, const I span)
template<class I>
void set_ang_pointer(const double *avec, const I span, const AngleUnit angle_unit)
void check_ang(const AngleUnit)
void check_hall_number(const int h)
void check_IT_name(const std::string &itname, const std::string &choice = "")

Protected Attributes

std::array<double, 3> len

basis vector lengths

std::array<double, 3> ang

basis vector angles ordered θ₁₂, θ₀₂, θ₀₁, in radian

double volume

volume of the unit cell formed by the basis vectors

Bravais bravais

Lattice centring type.

Symmetry spgsym

Spacegroup symmetry operators.

PointSymmetry ptgsym

Pointgroup symmetry operators.

Basis basis

The positions of all atoms within the unit cell.